Wheel slip occurs when the torque received from a vehicle's transmission exceeds the maximum reactive force that can be sustained by the friction between one or more of the vehicle's driven wheels and the road surface.
The prior art contains numerous examples of methods proposed to detect and/or to control wheel slip. The previously-disclosed methods involve detecting and/or collecting data that are expected or presumed to reflect whether a driven wheel is slipping or has lost traction with the road surface. The references cited are representative of those methods. These methods include:                Methods that detect what is believed to be excessive wheel speed;        Methods that detect what is believed to be excessive wheel acceleration;        Methods that determine vehicle speed from the speeds of the non-driven wheels;        Methods that determine linear vehicle acceleration;        Methods that determine lateral vehicle acceleration;        Methods that determine yaw rate from the angle of a vehicle's steering wheel;        Methods that determine yaw rate from accelerometers; and        Methods that attempt to estimate coefficients of friction between road surfaces and tires.        
By using one of these methods or more than one of these methods in combination, the inventions disclosed in the prior art generally operate by (i) ascertaining or modeling the path, velocity, or the trajectory of a vehicle to derive what the speeds of driven wheels are expected to be under those conditions when there is no loss of traction, (ii) comparing actual driven wheel speeds with expected driven wheel speeds, and (iii) deeming a driven wheel that exceeds in some specified degree its expected speed to be slipping or to have lost traction.
The methods of these inventions are essentially compromised because of the considerable range of differences between a vehicle's wheel speeds that are consistent with there being no slip or loss of traction whatever may be the path, velocity, or trajectory of the vehicle. In other words, the modeling is inherently imprecise, and the models' expected wheel speeds can only be approximations of actual wheel speeds. A vehicle's actual wheel speeds are influenced by many external factors which are unrelated to slip or loss of traction and which vary continuously. These external factors include, by way of examples, the path traveled, vehicle load, load distribution, surface gradient, surface camber, tire wear, tire dimensions, tire temperature, tire inflation, tire pressure, ambient temperature, type of road surface, road surface temperature, relative humidity, precipitation, surface contamination, etc.
As a result of the variability in wheel speeds deriving from those sources when the driven wheels are not slipping, estimates derived from modeling of what wheel speeds ought to be are not and cannot be very accurate, and the effect of their application to purport to detect slip or loss of traction is necessarily to create an illusion of certainty when the data employed to detect slip or loss of traction are inherently ambiguous. The problem of data ambiguity is not cured by looking at wheel speed differences, the acceleration of wheel speeds, or the acceleration of wheel speed differences because there are no thresholds that can be calculated that discriminate clearly between:                Wheel speeds, wheel speed differences, accelerations of wheel speeds, or accelerations of wheel speed differences that reflect the paths followed by the wheels or the differences in the paths followed by the wheels as a result of the turning of the vehicle and/or changes in the speed or acceleration of the vehicle: and        Wheel speeds, wheel speed differences, accelerations of wheel speeds, or accelerations of wheel speed differences that are indicative of wheel slip.        
In consequence:                There has to be a significant amount of uncertainty in relation to deeming a driven wheel that exceeds in some specified degree its expected speed to be slipping or to have lost traction based upon such modeling;        The uncertainty requires the methods of the prior art necessarily to declare the presence or absence of slip when such presence or absence is unavoidably ambiguous as a result of the nature of the modeling methods applied and the data utilized; and        The numerous traction control and differential control methods of the prior art are either always or most often too quick and excessively aggressive in reacting to wheel slip or too tardy and insufficiently aggressive in reacting to wheel slip.        
Stated differently, because the methods of the prior art cannot resolve the ambiguity inherent in their models and their data with precision, those methods must either, in the first case, err by waiting until the ambiguity resolves itself, and the wheel is clearly slipping, or, the second case, err by not waiting until the ambiguity resolves itself and prematurely declaring slip before it actually arises.                In the first case, the methods are not much good at detecting incipient slip;        In the second case, the methods presumably invoke anti-slip means when slip is not actually present;        In the first case, delay results in increasing slip as unreduced torque is applied to the slipping wheel, and the spinning up of the wheel makes getting the wheel back under control more difficult because the late or inadequately aggressive slip-prevention efforts will allow a vehicle to decelerate while an increasing amount of kinetic energy is added to the slipping wheel, and, while this combination of factors persists, the vehicle loses momentum; moreover, the loss of momentum tends to exacerbate the loss of traction, and the vehicle's operator is likely to react to this situation by increasing the power output of the vehicle's engine although doing so only increases the kinetic energy stored in the slipping wheel, which energy has to be dissipated to slow the wheel before that wheel can provide any significant tractive force; and        In the second case, the over-aggressive prevention of wheel speed difference imposes a continuous load on a vehicle's power-train that reduces the life of power-train components and increases fuel consumption; and in certain cases, over-aggressive prevention of wheel speed differences that should be permitted can also reduce vehicle stability.        
The inventors contend that:                Incipient slip can only be detected by utilizing higher derivatives of wheel speed differences;        Calculations of those higher derivatives must be based upon information received from the wheels themselves; and        Attempting to model expected wheel speeds, expected wheel speed differences, expected accelerations of wheel speeds, or expected accelerations of wheel speed differences is flawed.        
The foundation for these contentions is the fact that the only place where the friction between the road and a tire can be properly determined is where the tire is on the road and then only at that particular instant in time. In other words, the best information comes from the tire/wheel itself. The modeling methods of the prior art separate the detection of slip from the direct use of the information that comes from the wheel/tire itself, and this separation is the source of the estimation and ambiguity inherent in the modeling methods.
In the inventors' view, the essential problem, which is not solved by the prior art, is to devise a method of determining what the relationship between the wheel speeds ought to be under normal driving conditions even though those conditions have significant variability. The third derivative of actually measured wheel speed difference does precisely that and eliminates entirely or substantially entirely the ambiguity inherent in the methods disclosed in the prior art. The use of the third derivative of actually measured wheel speed difference avoids the separation of the detection of slip from the direct use of the information that comes from the tires/wheels themselves.
An examination of the behavior of the third derivative of wheel speed differences reveals that its value is or is near zero under all conditions except those conditions that involve slip or loss of traction.
The value of the use of the third derivative of wheel speed difference to detect slip or loss of traction derives from the facts that:                The third derivative of wheel speed difference provides a unitary threshold (value=0) for the detection of slip or loss of traction; and        The fact that the value of the third derivative of wheel speed difference varies from zero very materially when slip is present and varies from zero quite immaterially in the absence of slip.        
The inventors do understand that they are making the assumptions, in connection with the use of the third derivative of wheel speed difference to detect slip, that (i) all of the variables that do not reflect slip affect the tires fairly equally, and (ii) the only likely cause of a sudden change in wheel speed difference is the change in the coefficient of friction at a tire. The inventors believe that these assumptions are reasonable and well grounded.
The causes and consequences of the limitations of the teachings of the prior art include the following:                The prior art does not rely upon the data necessary to discriminate properly between characteristics of the wheels' rotation that indicate wheel slip and characteristics of the wheels' rotation that do not indicate wheel slip;        The prior art is not grounded in an understanding that a vehicle, and the vehicle's operator, have significant inertias that automatically determine the rates of change of wheel speed differences during normal vehicle travel, and that these inertias impose significant limits on the angular accelerations that a vehicle and its operator are subjected to during normal vehicle travel;        The prior art is not grounded in an understanding that the magnitudes of the higher derivatives of wheel speed difference during normal vehicle travel are significantly constrained by the limitations on the angular accelerations that are imposed on a vehicle and its operator by virtue of their inertias, and that magnitudes of the higher derivatives of wheel speed differences that lie beyond theses magnitudes are indications of slip; and        The prior art makes no reference to the use of the second or third derivative of wheel speed difference to detect slip or loss of traction and, in fact, teaches away from those approaches by complicating the analysis with diverse factors and modeling efforts.        
The use of second derivative of wheel speed differences to detect slip or loss of traction is not without value, but is not as useful as the third derivative because the value of the third derivative is zero in more cases than is the second derivative, and the second derivative has a constant non-zero value in certain cases.
The use of the third derivative of wheel speed differences to detect slip or loss of traction is wholly unanticipated by the prior art, is more effective for that purpose than the methods of the prior art, and is vastly simpler than the prior art for that purpose.
This application does not build upon the prior art. The teaching of this application is wholly distinguishable from the teaching of the prior art.